Reciprocal Screw Research Articles

Disain CAD Mekanisme Paralel Tiga Derajat Translasi Murni Dengan Rantai Kinematik Kombinasi Sambungan Revolut dan Prismatik


 
 
 
 In this study it was discussed kinematic design of a 3-RRRPP translational parallel mechanism. The design was carried out by using simulation performed using CAD software. Motion platform was analyzed based on screw and reciprocal screw theory. The evaluation mechanism performance was determined by introducing the stages of research in the form to determine mechanism parts such as base, links, and platform. The work was continued with the assembly process of each part. Furthermore, kinematic response represented by displacement of platform positions was figured out by a CAD simulation. Based on the results of the simulation, it was successfully designed the mechanism performing the translational motion of the Platform.
 
 
 
 
 

Kinetostatics of Deployable Concrete Formworks

Abstract To reform the traditional concrete formwork, an overconstrained deployable frame is designed. It is composed of closed-loop deployable units formed by scissor-form elements and orthogonal telescoping rods. Using the reciprocal screw theory, the mobility of the deployable frame is studied, and it has one degree of freedom (DoF). To analyze the kinematic performance of the frame in the deployment and folding processes and the static characteristics under external loads at different deployed states, a general approach to analyzing the kinematics and statics by modeling in screw form is proposed. The velocities of joints could be solved in screw coordinates, the position and acceleration of joints could be obtained via a first-order numerical integration and a first-order numerical differential interpolation, respectively. Then, the position information for each joint can be forwarded onto the static equilibrium equations. Through the static analysis at each deployed state, the inner forces in each rod and the active control forces are derived. Kinematics and statics are associated by using velocities as the global variable, which allows a unified analysis of mechanisms. This method is computationally highly efficient and also fits for kinematic and static analysis of different kinds of multi-rigid-body mechanisms.

Kinetostatics of a serial robot in screw form

Kinetostatics of a robot is an essential component of robotic analysis that includes actuation distribution and torque control. The extant methods mainly include the static transfer formulae and force Jacobian matrix algorithms based on the Denavit-Hartenberg (D-H) method. They can calculate the joint driving torque, but there are some limitations. This paper proposes a kinetostatics approach for analyzing the driving torque of serial manipulators. The instantaneous work done by the external load is expressed with reciprocal screw. It is the key idea of the approach to derive the kinetostatics equation in screw form and determine the required torque at each joint. This methodology is straightforward for programming. Through kinetostatic analysis of some typical serial manipulators, this paper shows the process of establishing the kinetostatics of every joint to calculate the torque in Plücker coordinates. The general spatial manipulator was analyzed and the solution demonstrates the universality of the method presented in this paper. In addition, the kinetostatic analysis method applies to all kinds of serial manipulators.

Dynamics of a 3-UPS-UPU-S Parallel Mechanism

In this paper, a parallel mechanism with two rotational degrees of freedom is proposed. It could rotate freely and continuously around the two coordinate axes at the fixed origin of the coordinate frame. The structure of the mechanism is a second-order over constraint parallel structure and the moving platform and base platform are connected by five kinematic chains. The motion characteristics of this structure are analyzed by reciprocal screw equation. Then, the kinematics and dynamics modelling are carried out systematically in a unified way. The kinematics of the mechanism is established by means of screws, the displacements and accelerations of each joint and any point on a link could be calculated by the kinematic screw equation directly. The analysis of acceleration and its mathematical expression in screw form are given, and the acceleration matrix could be applied into the dynamic analysis based on the Newton–Euler equation. All the constraint forces and torques could be obtained by a single set of Newton–Euler equations.

Kinematic modeling and analysis of transmission mechanism with joint clearance for flapping wing micro aerial vehicle

A theoretical model is built to reveal the effect of the joint clearance on the kinematic performance of the transmission mechanism of a flapping wing micro aerial vehicle (FWMAV). Massless link approach is used to model the joint clearance and the reciprocal screw is introduced to solve the kinematic model. Finite element method simulations are also performed to validate the model. The kinematic model reveals that the inertia force of the transmission mechanism contributes little to the flapping motion whereas the sign of the resultant moment of aerodynamic drag and wing inertia force plays decisive role. Besides, the joint clearance can either increase or decrease the flapping angle of the wing during a flapping period and it will significantly affect the flapping amplitude while involves little in the mean flapping angle. The effects of the positions of the joint with clearance and its magnitude on the flapping motion are also revealed.

Velocity and Singularity Analysis of a 5-DOF (3T2R) Parallel-Serial (Hybrid) Manipulator

This article presents the velocity and singularity analysis for a five-degree-of-freedom (5-DOF) parallel-serial manipulator. The hybrid structure of the manipulator combines a tripod-like parallel part and a serial part, represented as two carriages moving in perpendicular directions. This manipulator provides its end-effector with a 3T2R motion pattern, which includes three independent translations and two independent rotations. First, the study briefly discusses the manipulator design and the results of the position analysis. These results form the basis for the subsequent velocity and singularity analysis, performed by screw theory. The screw coordinates of the unit twists are written for each manipulator joint, and then through the reciprocal screw approach, the actuation and constraint wrenches of the manipulator are obtained by simple inspection. Based on these twists and wrenches, the paper forms the velocity equation and shows an example of the inverse velocity analysis for a given end-effector trajectory. The same example is solved by numerical differentiation to verify the proposed approach. Next, the paper investigates singular configurations by analyzing the wrench system of the manipulator and presents several conditions for serial and parallel singularities. Each condition has both a symbolic representation, given by an equation for screw coordinates of certain wrenches, and a visual representation, which shows the manipulator in a singular configuration.

Forward Kinematics and Singularity Analyses of an Uncoupled Parallel Manipulator by Algebraic Screw Theory

In this contribution, the Jacobian analysis of a four-legged six-degrees-of-freedom decoupled parallel manipulator is carried out through the screw theory. As an intermediate step, for the sake of completeness the inverse/forward displacement analysis as well as the computation of the workspace of the robot are achieved by taking advantage of the decoupled orientation and position of the moving platform. Afterward, the input/output equation of velocity of the parallel robot is obtained by harnessing of the properties of reciprocal screw systems. Once the Jacobian matrices are identified and investigated, the analysis of singularities for the robot manipulator emerges as a natural application of the Jacobian analysis. Numerical examples are included with the purpose to show the practicality and versatility of the method of kinematic analysis. Furthermore, the numerical results obtained by means of the theory of screws are successfully verified with the aid of commercially available software like ADAMS.

Revisiting screw theory-based approaches in the constraint wrench analysis of robotic systems

AbstractThis paper aims at shedding lights on two approaches that were recently proposed for the constraint wrench analysis of robotic manipulators. Both approaches benefit from the Newton–Euler equations, screw notations, and constraint transformation matrices (CTM) to cope with the inverse dynamic problem of multibody systems. In the first approach, which is called the joint-based method, the constraint transformation matrices are derived directly from the kinematic constraints which are imposed on the rigid links by kinematic pairs. In the second approach, which is referred to as the link-based method; however, the constraint matrices are obtained based on the wrench transfer formula of each rigid link. In this study, by resorting to the definition of reciprocal screws, the former methodology is further enhanced to a new version as well. Moreover, based on the proposed modified joint-based CTM, constraint forces and moments distribution indices are introduced. The three constraint wrench analysis methodologies, two joint-based and one link-based, result in different CTMs and set of equations as well, which will be discussed in detail. In the end, on two case studies, a spherical four-bar linkage and a Delta parallel robot, the pros and cons of all three constraint wrench analysis methodologies are discussed, and the proposed indices will be examined. The numerical results reveal that, although all three methods identically compute the magnitude of the applied and constraint force and moment vectors, the joint-based approaches do not report the constraint components with respect to a specific coordinate frame. Moreover, it is shown that the proposed indices can approximately predict the constraint forces and moments distribution at joints, which can be used as force transmission indicators in multibody systems.

Type synthesis of plane-symmetric deployable grasping parallel mechanisms using constraint force parallelogram law

Type synthesis methods of parallel mechanisms or metamorphic mechanisms have drawn rising interest for mechanism designers. However, existing synthesis approaches cannot synthesize both parallel mechanisms and metamorphic mechanisms. This paper develops a synthesis method of metamorphic mechanisms, which enables it to construct a family of 2-degree-of-freedom (DOF) deployable grasping parallel mechanisms. Namely, the originality of this paper is that it explores a common synthesis method for both parallel mechanisms and metamorphic mechanisms. First, a new type of grasping sub-mechanisms is designed. Then, a kinematic sub-chain is constructed after assembly of a base, a platform, and the grasping sub-mechanism, whose constraint-screw system is obtained using reciprocal screw theory. This constraint-screw system is further applied to derive the desired constraints of auxiliary sub-mechanisms using the constraint force parallelogram law. Subsequently, auxiliary sub-mechanisms are type synthesized based on such desired constraints. Finally, a class of parallel mechanisms is constructed by assembling the auxiliary and the kinematic sub-chain. Thus, this paper and related work generate fresh insight into synthesizing both single-DOF metamorphic mechanisms and 2-DOF parallel mechanisms.

Feasibility, planning and control of ground-wall transition for a suctorial hexapod robot

One of the key factors that affect the efficiency and scope of work of wall-climbing robots is how the climbing robot can achieve autonomous transition between adjacent vertical planes. This paper studies the problem of ground-wall transition of a self-developed suctorial wall-climbing hexapod robot (WelCH). In view of the feasibility of the robot performing transition, this paper makes a detailed analysis of the number and property of degrees of freedom (DOFs) of the body and the foot based on reciprocal screw theory, and the results show that the robot can achieve transitional motion only when its home configuration is axisymmetric rather than radially symmetric. For realizing the robot’s ground-wall transition, based on a Sinusoid-Sigmoid-Shaped (SS-Shaped) interpolation function, the motion strategies of foot transferring and body pitching are firstly designed in detail. This interpolation method can effectively avoid the wear of the suction cups by relying on fewer essential path points. Then, the saturation-truncated method and mean filtering method are used to deal with joint constraints and abrupt changes in angular velocities. Finally, a kinematic-based adaptive sliding mode control (ASMC) is adapted to track the planned smooth trajectory, which can effectively resist bounded external disturbances. The successful transitions from the horizontal ground to the vertical wall for the robot WelCH in simulation and filed experiment demonstrate the effectiveness of the proposed strategy.

Stiffness modeling of n(3RRlS) reconfigurable series-parallel manipulators by combining virtual joint method and matrix structural analysis

Stiffness is one of the critical performance indexes for robotic manipulators. In this study, a method for establishing the stiffness models of n(3RRlS) reconfigurable series-parallel manipulators (RSPMs) is proposed by combining the virtual joint method and matrix structural analysis. First, the constraint wrench system of the 3RRlS reconfigurable parallel manipulator (RPM) is obtained based on the reciprocal screw theory. Second, the stiffness matrices of the limbs along the axes of the constraint wrenches are analyzed using matrix structural analysis, and the overall stiffness matrix of the limbs is then assembled. Third, the stiffness matrices of the 3RRlS RPM and the n(3RRlS) RSPM are successively derived using the principle of virtual work. Finally, the theoretical and the finite-element-analysis deformations of the 3RRlS RPM and 3(3RRlS) RSPM are solved, and their average relative error is within 3.78%. It can be concluded that increasing actuation constraints can effectively improve the stiffness of manipulators in the directions of six degrees of freedom (DOFs) while increasing structural constraints can effectively improve the stiffness of manipulators in the directions of constrained DOFs.

Kinematics analysis of a novel 2R1T 3-PUU parallel mechanism with multiple rotation centers

In this paper, we present a novel three-degree-of-freedom (3-DOF) 3-PUU parallel mechanism (PM) with multiple rotation centers. Having two rotational DOFs and one translational DOF, the 3-PUU parallel robot consists of a fixed platform, a movable platform, and three identical PUU branches. Each PUU branch is composed of one prismatic(P) joint and two universal(U) joints. The mobility of initial configuration of the 3-PUU PM is analyzed using the reciprocal screw theory. Analysis of the 3-PUU PM's mobility of general configuration is performed based on its geometrical characteristics. The movable platform of the 3-PUU PM is demonstrated to be capable of rotating around multiple points. The singularities of 3-PUU PM are discussed. Using the inverse kinematics method, the workspace is obtained. Numerical examples are provided to illustrate the motion characteristics of the 3-PUU PM as a mechanism with multiple rotation centers.

PyScrew4Mobility: Modul Python untuk Penentuan Mobilitas Manipulator Paralel Berbasis Teori Screw

This paper addresses the mobility determination of parallel manipulators (PMs) using screw theory with algebra methods on an open-source computer algebra package: Sympy (symbolic python). The screw theory can specify the number and the type of motions owned by PMs with over-constrained or non-over constrained kinematic structures. The algebra methods are applied to obtain reciprocal of a screw or a screw system and basis of a screw system using null-spaces and the row/column-spaces technique, respectively. Hence, an object-oriented python module, called a pyScrew4Mobility module, is designed to realize such implementation. The module consists of three classes namely a Screw, a ScrewSystem and a ManipulatorMobility. A screw is constructed by the class of Screw, including its algebraic calculation such as negation, addition, multiplication, and product of two screws. Then, the ScrewSystem is used to construct a system of screws. It can be used to find reciprocal screws, unique screws within the system of screws, and calculate the products of two systems of screws. The last class or ManipulatorMobility has a direct implementation to determine the mobility of PMs. It uses information from the list of unit screw direction, position, and pitch. Finally, the designed screw module is tested to demonstrate its capability to determine the mobility of four well-known PMs, i.e. 3-PRRR; 3-PR(Pa)R; 4-PRRU; and 6-UPS, including the respective time spent for calculation.

Type synthesis of overconstrained 2R1T parallel mechanisms with the fewest kinematic joints based on the ultimate constraint wrenches

“Two rotational degrees of freedom” and “one translational degree of freedom” (2R1T) parallel mechanisms (PMs) have been successfully applied to develop five-axis hybrid robots for machining purposes. However, the number of passive joints contained in current 2R1T PMs has not still reached the minimum, which may impede these robots from having high stiffness. This study has put forward the concept of ultimate constraint wrenches acting on the PM's moving platform, and this concept was used to reduce the number of kinematic joints to a minimum. Based on the reciprocal screw theory, an ultimate constraint wrench system of the 2R1T PMs was found, and then a series of novel overconstrained 2R1T PMs with the fewest kinematic joints, containing three or four branches, were constructed. Furthermore, based on a developed overconstrained four-branch 2R1T PM RPU-2UPR-RPR, a type of five-axis hybrid robot with the fewest kinematic joints was constructed, which demonstrated good application prospects.

Fundamental equation of mechanism kinematic geometry: Mapping curve in se(3) to counterpart in SE(3)

The most general continuous rigid motion can be described by a curve in SE(3) of whose tangent vector the left or right invariant representation is a curve in se(3). The integral operation between them has not been achieved because there is no general solution for a system of the first-order linear differential equations with variable coefficients in mathematics. This paper develops a matrix equation (termed as the fundamental equation) based on the geometric properties of a pair of conjugate axodes equivalent to a curve in se(3) in algebras to achieve this integral operation. Moreover, the first-order and second-order derivations of the fundamental equation are derived. Furthermore, an algebraic method representing the body and spatial velocity twists as vector functions of dimensions and input parameters of mechanisms is founded on the theory of reciprocal screws. After that, this method and the fundamental equation are validated by the numerical examples of Bennett, spherical and planar four-bar linkages. Finally, this work presents a notion of generalized-involute which is a useful tool in the study of gear tooth profile and cam profile.

Modelling and analysis for a cylindrical net-shell deployable mechanism

Existing cylindrical deployable structures have poor controllability of deployment or weak bearing capacity. In order to satisfy the application needs of cylindrical deployable structures in the space industry, a cylindrical net-shell deployable mechanism is established in this article. The proposed cylindrical net-shell deployable mechanism has a regular cuboid shape in the folded state and a truss structure in the deployed state, and it can fit cylindrical surface, parabolic cylindrical surface, sine cylindrical surface and so on. Furthermore, based on reciprocal screw theory and screw synthesis theory, the mobility of cylindrical net-shell deployable mechanism in the whole motion cycle is analysed by the proposed equivalent model method. Results show that the cylindrical net-shell deployable mechanism is a single-degree-of-freedom mechanism. Moreover, a prototype is manufactured, and its motion performance is tested. The experiment shows that the cylindrical net-shell deployable mechanism has a smooth motion performance, and the mobility analysis method for complex coupled mechanism in this study is valid. This study has a certain significance in expanding the application field of cylindrical shell structure.

A New Mathematical Method to Study the Singularity of 3-RSR Multimode Mobile Parallel Mechanism

In the process of parallel mechanism design, it is difficult to avoid the singularity, especially in the mobile parallel mechanism. Therefore, a new mathematical method to study the singularity of multimode mobile parallel mechanism is proposed. In this paper, the singularity of 3-RSR parallel mechanism (PM) is analyzed by using reciprocal screw methods and linear geometry theory from two aspects of fixed mode and all-attitude multiple motion modes. Specifically, the complete Jacobian matrix of the PM is obtained by using the screw theory, and the reciprocal screw of each branch is expressed with algebraic method and geometric drawing method. Furthermore, the singularity of the PM can be obtained by analyzing the reciprocal screw correlation and using the spatial linear geometry theory. Finally, we analyze the singular configuration of the PM under various modes, which provide theoretical guidance for the gait planning of the multimode mobile PM and will be useful for the selection of mechanism drive and time-sharing control.

Application of Screw Theory to the Analysis of Instant Screw Axis of Vehicle Suspension System

This paper proposes a method using screw theory to find the twist of a rigid body of a mechanism. For this, a geometric method to determine the screws and reciprocal screws associated with kinematic joints and links is introduced. This geometric method provides a simple way to find the wrenches acting upon a rigid body of a mechanism using the joint types and positions. Then, the twist which is reciprocal to the wrenches is determined to find the instant screw axis and pitch of the body. The proposed method is applied to planar mechanisms and spatial suspension mechanisms. For planar mechanisms, the method finds the instant center of velocity as the point in the plane of planar motion intersected by the instant screw axis. Using the proposed method, the instant screw axes and pitches are determined for the bump-rebound motion and steering motion of the double wishbone, McPherson strut, and 5-SS multi-link type suspension mechanisms. The numerical results agree with findings of previous researches.

Task-oriented type synthesis of the lower-mobility parallel mechanisms with a common platform

A systematic procedure for the task-oriented type synthesis of parallel mechanisms (PMs) with a common platform is proposed in this study. The method is composed of two stages. In the first stage, constraint wrenches that are compatible to specific task-oriented output motions of the PM is distributed to several limbs. In the second stage, the geometric conditions and admissible joint structures of PM limbs are identified by employing the concept of reciprocal screw. Then desired symmetric or asymmetric PMs are constructed with the proper combinations of those admissible limbs. Lastly, the suggested synthesis method is verified by identifying various forms of lowermobility PMs, such as planar 1T-type PMs, spatial 2T-type PMs and spatial 1T2R-type PMs.

Design and kinematic analysis of a spherical parallel manipulator using concurrent planar parallelogram linkages

This paper presents the design of a novel spherical parallel manipulator. The spherical parallel manipulator consists of three identical limbs and each of them is formed by a planar parallelogram linkage, a universal joint, and a revolute one, successively. Its mobility is analyzed using the reciprocal screws. After that, the kinematics is analyzed in detail, including inverse kinematic modeling, which is validated by a numerical example, inverse Jacobian analysis, singularity analysis, and manipulability analysis, which shows a relatively good performance of force transmission. Then based on the analysis, one prototype is fabricated to validate the effectiveness and feasibility of the design. In the end, some conclusions are drawn and future works are discussed.